Ask a biologist

[nihilistcat]

Okay I guess I'll play, gotta be a good sport and all.

Molecular biologist here ... ask me anything about biology (evolution, cancer research, genetic engineering, whatever)!

Can a DNA molecule partially split and be able to attach to a longer string or another partially split string?

Yes absolutely. DNA suffers all sorts of damage, including single or double stranded breaks, and they can attach to other strands (e.g. non-homologous end joining). 

We do have DNA repair mechanisms that can repair breaks, but our DNA repair mechanisms, although incredibly accurate, are not perfect. The repair process itself can lead to mutations, or this type of damage (if not repaired) can lead to cell death. In the rare case where a mutation confers a survival advantage over adjacent cells, it can lead to cancer.